Generators selected (1); t(1, 0, 0); t(0, 1, 0); t(0, 0, 1); (2); (4)
Multiplicity, Wyckoff letter,
Site symmetry | Coordinates |
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| | (1) x, y, z | (2) -y, x - y, z + 1/3 | (3) -x + y, -x, z + 2/3 | | (4) -x, -y, z + 1/2 | (5) y, -x + y, z + 5/6 | (6) x - y, x, z + 1/6 |
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I Maximal translationengleiche subgroups
| [2] P31 (144) | 1; 2; 3 |
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| [3] P21 (4, P1121) | 1; 4 |
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II Maximal klassengleiche subgroups
[3] a' = 3a, b' = 3b
 | H61 (169, P61) | <2; 4> | a - b, a + 2b, c | | | H61 (169, P61) | <2 + (1, -1, 0); 4 + (2, 0, 0)> | a - b, a + 2b, c | 1, 0, 0 | | H61 (169, P61) | <2 + (2, -2, 0); 4 + (4, 0, 0)> | a - b, a + 2b, c | 2, 0, 0 |
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[4] a' = 2a, b' = 2b
 | P61 (169) | <2; 4> | 2a, 2b, c | | | P61 (169) | <2 + (1, -1, 0); 4 + (2, 0, 0)> | 2a, 2b, c | 1, 0, 0 | | P61 (169) | <2 + (1, 2, 0); 4 + (0, 2, 0)> | 2a, 2b, c | 0, 1, 0 | | P61 (169) | <2 + (2, 1, 0); 4 + (2, 2, 0)> | 2a, 2b, c | 1, 1, 0 |
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- Series of maximal isomorphic subgroups
[p] c' = pc
| P65 (170) | <2 + (0, 0, 2p/3 - 1/3); 4 + (0, 0, p/2 - 1/2)> | a, b, pc | | | | p > 4; p ≡ 5 (mod 6)
no conjugate subgroups |
| P61 (169) | <2 + (0, 0, p/3 - 1/3); 4 + (0, 0, p/2 - 1/2)> | a, b, pc | | | | p > 6; p ≡ 1 (mod 6)
no conjugate subgroups |
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[p2] a' = pa, b' = pb
| P61 (169) | <2 + (u + v, -u + 2v, 0); 4 + (2u, 2v, 0)> | pa, pb, c | u, v, 0 | | | p > 1; 0 ≤ u < p; 0 ≤ v < p
p2 conjugate subgroups for prime p ≡ 2 (mod 3) |
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[p = q2 + r2 + qr] a' = qa - rb, b' = ra + (q + r)b
| P61 (169) | <2 + (u, -u, 0); 4 + (2u, 0, 0)> | qa - rb, ra + (q + r)b, c | u, 0, 0 | | | q > 0; r > 0; p > 2; 0 ≤ u < p
p conjugate subgroups for each pair of q and r |
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I Minimal translationengleiche supergroups
II Minimal non-isomorphic klassengleiche supergroups
- Additional centring translations
| [2] c' = 1/2c P62 (171); [3] c' = 1/3c P63 (173) |
